2010
DOI: 10.1007/s00208-010-0489-3
|View full text |Cite
|
Sign up to set email alerts
|

On logarithmic extension of overconvergent isocrystals

Abstract: In this paper, we establish a criterion for an overconvergent isocrystal on a smooth variety over a field of characteristic p > 0 to extend logarithmically to its smooth compactification whose complement is a strict normal crossing divisor. This is a generalization of a result of Kedlaya, who treated the case of unipotent monodromy. Our result is regarded as a p-adic analogue of the theory of canonical extension of regular singular integrable connections on smooth varieties of characteristic 0.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

1
59
0

Year Published

2010
2010
2022
2022

Publication Types

Select...
6

Relationship

2
4

Authors

Journals

citations
Cited by 14 publications
(60 citation statements)
references
References 12 publications
1
59
0
Order By: Relevance
“…is in fact an isomorphism of (R K , ∇)-modules. Following [Ked07, 3.6.2] (this is more explicitely written in [Shi10,2.12] and also more general), since F ]Z[ is log-convergent then F ]Z[ is unipotent. Hence, the canonical morphism can :…”
Section: (Unipotence and Consequences)mentioning
confidence: 99%
“…is in fact an isomorphism of (R K , ∇)-modules. Following [Ked07, 3.6.2] (this is more explicitely written in [Shi10,2.12] and also more general), since F ]Z[ is log-convergent then F ]Z[ is unipotent. Hence, the canonical morphism can :…”
Section: (Unipotence and Consequences)mentioning
confidence: 99%
“…Also, we recall several results proved in [19]. In this section, we fix an open immersion X → X of smooth k-varieties with Z := X − X = r i=1 Z i a simple normal crossing divisor (with each Z i smooth and irreducible) and let us denote the log structure on X associated to Z by M X .…”
Section: Overconvergent Isocrystals and Log-extendabilitymentioning
confidence: 99%
“…1.5 in this paper.) In the previous paper [19], we introduced the notion of 'having -unipotent monodromy' for an overconvergent isocrystal on (X, X )/K and proved that an overconvergent isocrystal on (X, X )/K has -unipotent monodromy if and only if it can be extended to an isocrystal on the log convergent site ((X , M X )/O K ) conv with exponents in . In this paper, A. Shiho (B) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan e-mail: shiho@ms.u-tokyo.ac.jp we prove a 'cut-by-curves criterion' for an overconvergent isocrystal on (X, X )/K to have -unipotent monodromy.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations